But didn't we already know that NN can solve any computable problem? The interesting thing is if they can be trained to solve any (computable) problem.
But recurrent neural networks can do solve any computational problem given enough precision.
I got to admit, I'm sorta sticking to that at face value, because I don't know enough computer science to a) discern if that is true and b) know what "f: X -> Y only for closed domains" means.
When you only have a fixed width, ie. a static feed forward network, you have an upper limit to the data you can represent and compute on.
Eg. if the highest number you can represent is 1.000, then you will need a new NN if you want to do computations on 1.001.
... or use an inductive structure, like a recurrent neural network has.
How would that compare with a biological neural network with presumably near-infinite precision ?